Each time you visit the NRICH site there will be some activities which are 'live'. This means we are inviting students to send us solutions, and we will publish a selection of them, along with each student's name and their school, a few weeks later. If you'd like to know more about what we're looking for, read this short article.
Live problems
No live problems at the moment
Recently solved problems
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problemFavouriteCharlie's delightful machine
Age11 to 16Challenge level
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
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problemFavouriteSlick Summing
Age14 to 16Challenge level
Watch the video to see how Charlie works out the sum. Can you adapt his method?
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problemFavouriteCyclic Quadrilaterals
Age11 to 16Challenge level
Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?
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problemFavouriteTilted Squares
Age11 to 14Challenge level
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
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problemFavouriteCuboid Challenge
Age11 to 16Challenge level
What's the largest volume of box you can make from a square of paper?
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problemFavouriteTake Three From Five
Age11 to 16Challenge level
Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?
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problemFavouriteM, M and M
Age11 to 14Challenge level
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
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problemFavouriteHave you got it?
Age11 to 14Challenge level
Can you explain the strategy for winning this game with any target? -
problemFavouriteAdd to 200
Age11 to 14Challenge level
By selecting digits for an addition grid, what targets can you make? -
problemFavouriteWipeout
Age11 to 16Challenge level
Can you do a little mathematical detective work to figure out which number has been wiped out? -
problemFavouritePick's Theorem
Age14 to 16Challenge level
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.